# What is the limit of #cosx# as x goes to infinity?

There is no limit.

Recall or Note:

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Refer to explanation

Choose two sequences such as

The theorem that was used for the proof is

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The limit of cos(x) as x goes to infinity does not exist.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the limit of #((e^(2z))-1) / (e^z)# as z approaches 0?
- How do you determine the limit of #(3/x^3 - 6/x^6)# as x approaches 0-?
- How do you find #lim sqrt(x^2+x)-x# as #x->oo#?
- What is the limit of #(x + (sqrt(x^2 + 2x))# as x goes to negative infinity?
- How do you use the Squeeze Theorem to find #lim sqrt(x^3+x^2) * sin (pi/x) # as x approaches zero?

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